There are a variety of applications that incorporate the use of three-dimensional data. In a non-discrete form, this three-dimensional data may be represented as a three dimensional contour that includes a plurality of peaks. In a discrete form, this three-dimensional data may take the form of a series or array of elements. In such an array, each element would include three values corresponding to the three dimensions of the contour.
In the various applications that incorporate the use of three-dimensional data, it may be desirable to determine peak summits, also referred to as “maxima” in the data. For example, in a manufacturing environment, numerical optimization methods are used to determine optimal values for process variables where closed form equations are not available to do so. According to the numerical optimization methods, process variables are adjusted incrementally while a property of the manufacture dependent on the variables is recorded. The combination(s) of process variables that produce the desired property of the manufacture may then be selected as optimal values for the particular process.
Illustrative of these methods, take for example a manufacturing process wherein a property of a manufactured product, such as thickness, varies depending on process variables, such as temperature and pressure. In the manufacturing process, both the temperature and pressure are maintained within predetermined ranges. Within these ranges, certain combinations of temperature and pressure produce an optimal, e.g., maximum, thickness in the product. In order to determine the temperature and pressure combination(s) that produce this maximum thickness, a three-dimensional array of data is recorded wherein temperature and pressure are represented in two of the dimensions and thickness is represented in the other dimension. Peak summits (i.e., maxima) in the thickness dimension can thus be associated with a particular combination of temperature and pressure.
Illustrative of another application that incorporates the use of three-dimensional data, the determination of peak summits in the data comprises a step in a process for determining the location of emitters of electromagnetic (“EM”) radiation in a monitored area, such as a geographic area. Such an application may be desirable, for example, in a military or security setting. In this particular application, electromagnetic radiation data is collected simultaneously at a plurality of EM receiver platform sites having known locations in the monitored area.
Known methods for locating EM emitters determine the time difference of arrival (“TDOA”) and/or frequency difference of arrival (“FDOA”) of the electromagnetic radiation data collected at the EM receiver platforms. TDOA relates to the time shift in receiving the EM data at the various EM receiver platforms. TDOA results from, among other things, differences in the signal path length between the emitters and receivers and differences in signal propagation mediums. FDOA relates to a frequency shift or Doppler shift in the EM data received at the various EM receiver platforms. FDOA results from, among other things, movement of the emitters and/or receivers.
In the known methods, TDOA and/or FDOA data collected at two EM receiver platforms is used to generate three-dimensional data in the form of a contour representative of the EM radiation in the monitored area of interest. The number of generated contours can be increased by increasing the number of EM receivers used to collect the data. For example, if there are three EM receivers (e.g., receivers A, B, and C), a first surface can be generated using TDOA/FDOA data collected at receivers A and B, a second surface can be generated using TDOA/FDOA data collected at receivers B and C, and a third surface can be generated using TDOA/FDOA data collected at receivers A and C.
In the contours, time shift (τ) and frequency shift (ν) are typically represented on the horizontal axes and the magnitude of the detected electromagnetic radiation is represented on the vertical axis. If there is no FDOA (i.e., if the emitters and receivers are stationary), then the frequency shift (ν) is zero. “Peaks” on the contour having an EM radiation level above a predetermined threshold are determined to be indicative of EM emitters. The predetermined threshold is determined as a function of factors such as electromagnetic noise levels in the monitored area. Electromagnetic noise is a function of a variety of factors, such as the number of EM emitters in the monitored area of interest.
In this particular application, the locations of the EM emitters are associated with the peak summits on the contour. Once the location of the peak summit is determined, the time shift τ and frequency shift ν associated with that location is recorded. This data is used to generate curves indicative of constant time and/or frequency paths for each potential emitter. Thus, in the example set forth above, three sets of curves (one for each of contours A–B, B–C, and C-A) would be calculated. In each set of curves, there would be a constant time/frequency path curve for each EM emitter. In order to determine the EM emitter locations, curves calculated using data from two of the contours (e.g., contours A–B and B-C) are compared to determine where the curves intersect. These intersections indicate potential EM emitter locations.
The peak summits on the contour are typically located using known numerical search and estimation techniques. In one such known technique, numerical searches are conducted from starting points that are adjusted incrementally over the contour to determine if the starting point is a peak summit. For several reasons, however, these methods are inefficient and can lead to inaccurate results. One source of inefficiency stems from the fact that these methods perform multiple iterations of the search routine on the same data. Other inefficiencies and/or inaccuracies depend on the selection of the step size of the increments and the starting point of the routine. If the step size is too large, peak summits and even entire peaks can be missed completely, thus producing an incomplete solution set. If the step size is too small, peak summits may be found multiple times, and thus may require an unacceptably high processing capacity or produce a slow processing time.
These inefficiencies are compounded where there are a multiple peaks on the contour and where there is a large three-dimensional data space to analyze. Factors such as noise levels in the monitored area can further complicate the process. Such complexity is undesirable for obvious reasons, such as processing speed, system expense, etc.